The principle for linear FMCW radar is well-known, see for example Skolnik, Introduction to Radar Systems, 2nd Ed., McGraw-Hill 1980, Chapter 3. Technical advances have in recent years resulted in an increased use of FMCW radar units, which will not be considered further here. A linear FMCW (Frequency Modulated Continuous Wave) radar unit works in principle as follows:
A frequency sweep controls an oscillator with a variable frequency so that the transmitted frequency varies periodically. Each period has principally three parts, namely a constant base frequency, a linear frequency sweep and a rapid return to base frequency. The linear frequency sweep is the time when the radar unit is "carrying out useful work" and often constitutes 70-80% of the total time (work factor 0.7-0.8).
For the sake of simplicity in the discussion below the radar unit and its target are stationary. In the case of moving targets or moving radar units the Doppler effect also comes into play. For most actual FMCW systems however, the Doppler effect only involves a minor correction to the following.
The propagation time from the radar unit to a target and back again is typically a few microseconds. A signal received from a target has therefore the frequency that was transmitted a certain time before. As the frequency is swept this is not the same frequency that is being transmitted. The received frequency also has a linear frequency sweep. As the received frequency sweep and the transmitted frequency sweep are parallel with a time-displacement equal to the propagation time, as a result for a fixed target the difference in frequency between the transmitted and received signal will be constant. This constant frequency difference is given by the product between the propagation time to the target and the gradient of the frequency sweep expressed as frequency per unit of combining time.
The signal processing in a linear FMCW radar unit consists principally of the transmitted and received signals, so that the difference signal (the beat signal) is generated. This signal is the sum of a number of sine waves, where each sine wave represents a radar target. The sine waves have different frequencies, amplitudes and phase positions in accordance with the principle that large amplitude corresponds to large target, high frequency corresponds to target at a great distance. The Doppler effect (due to the relative speed) mainly affects the phase positions.
In order to determine what targets are being observed and what are their sizes and relative speeds, the difference signal is frequency-analyzed. The frequency analysis is best carried out digitally by passing the difference signal through an anti-alias filter and sampling at a constant sampling rate, after which the sampled signal is multiplied by a window function to reduce the amplitude of the signal at the start and end of the sampling period and is sent to a signal processor that carries out a Discrete Fourier Transform, DFT, usually with a fast algorithm, known as an FFT, Fast Fourier Transform. The Fourier Transform is generally complex but for a real time signal (difference signal) it has a certain degree of symmetry. In order to be able to use FFT algorithms the number of samples is usually selected as a power of two (256, 512, 1024, . . . . ). 256 samples give 256 FFT coefficients, but if the signal is real the symmetry means that of these 256 values only 128 (actually 129) are independent.
By Fourier Transform, for example by FFT, the signal is divided into a number of discrete frequency components, sines. Each frequency corresponds as above to a distance. The amount of a complex FFT coefficient is a measurement of the radar target area (the received power) for the target in the corresponding frequency window (distance window). The FFT performs what is known as a coherent integration of the target signal, which is advantageous. The subsequent signal processing in the system is carried out digitally on the calculated FFT coefficients.
It can be shown that the nominal width of a distance window is inversely proportional to the change in frequency of the linear FMCW sweep during the sampling period. For a distance resolution of 1 m a change in frequency of 150 MHz is required. In order to change the distance resolution, the gradient of the frequency sweep can for example be changed while retaining the same constant sampling time.
The sampling rate limits the frequencies of the beat signal that can be studied and thereby the total observed distance area. The width of this "useable band" that lies parallel to the linear FMCW sweep is often less than 1 MHz.
A linear FMCW radar unit can be subject to interference if it receives signals other than its own transmitted signals reflected from various targets. The radar unit can be subject to interference from other radar units, including pulse radar units, pulse compression radar units and other FMCW radar units. Interferences of short duration arise for instance when the linear sweep in the FMCW radar unit is subject to interference from base frequencies or return frequencies from another FMCW radar unit.
An interference of short duration (a pulse) during the sampling period has a short extent in the time domain and is very broad-band in the frequency domain. A short but strong interference affects only a few samples of the beat signal but can totally mask many frequency windows in the Fourier Transform. The "noise level" in the Fourier Transform can appear to be increased, so that small targets can be masked by the interference.
A known method for suppressing interferences of short duration is to eliminate the interference by inserting a low value, e.g. 0, ("clipping") during the time the interference is detected. Clipping to 0 can in itself eliminate the interference from the time signal but introduces instead interference in the complex FFT, as the useable signal is also affected. Among other things targets with strong contrast are widened (get side beams). The interferences in the FFT can be modified, but never eliminated, by means of various compromises in the implementation of the clipping.